Approximate and generalized confidence bands for the mean and mode functions of the lognormal diffusion process

Approximate and generalized confidence bands for the mean and mode functions of the univariate lognormal diffusion process are obtained. To this end, the already existing methods for building confidence intervals for the mean of the lognormal distribution have been suitably adapted. Moreover, a new method has been proposed. The bands obtained from the above procedures are compared through a simulation study and the comparisons are made both in terms of coverage errors and average widths. This comparative study allows to choose the most appropriate confidence band for each particular case in practical situations. This is shown in an application to a real data set.